Simple arguments predict that the dynamics of a dissolved macromolecule confined to a channel comparable to its equilibrium coi size (~1 um for viral DNA) are quite different from those in free solution, because of the no-slip boundary condition on the fluid motion. Nevertheless, detailed, predictive computations have not been previously performed. We have incorporated a Brownian dynamics model of DNA into a fully self-consistent computational scheme that simultaneously resolves the macromolecular and fluid (i.e. solvent) dynamics of DNA in a microfluidics channel. The key novel feature of this scheme is the numerical computation of the Green's function for the flow problem, enabling a stochastic solution method that incorporates detailed hydrodynamics and respects the fluctuation-dissipation theorem. With this methodology we study a number of important confinement effects, focusing here on the retardation of relaxation of a chain in small channel.